A signed distance function (SDF) as the 3D shape description is one of the
most effective approaches to represent 3D geometry for rendering and
reconstruction. Our work is inspired by the state-of-the-art method DeepSDF
that learns and analyzes the 3D shape as the iso-surface of its shell and this
method has shown promising results especially in the 3D shape reconstruction
and compression domain. In this paper, we consider the degeneration problem of
reconstruction coming from the capacity decrease of the DeepSDF model, which
approximates the SDF with a neural network and a single latent code. We propose
Local Geometry Code Learning (LGCL), a model that improves the original DeepSDF
results by learning from a local shape geometry of the full 3D shape. We add an
extra graph neural network to split the single transmittable latent code into a
set of local latent codes distributed on the 3D shape. Mentioned latent codes
are used to approximate the SDF in their local regions, which will alleviate
the complexity of the approximation compared to the original DeepSDF.
Furthermore, we introduce a new geometric loss function to facilitate the
training of these local latent codes. Note that other local shape adjusting
methods use the 3D voxel representation, which in turn is a problem highly
difficult to solve or even is insolvable. In contrast, our architecture is
based on graph processing implicitly and performs the learning regression
process directly in the latent code space, thus make the proposed architecture
more flexible and also simple for realization. Our experiments on 3D shape
reconstruction demonstrate that our LGCL method can keep more details with a
significantly smaller size of the SDF decoder and outperforms considerably the
original DeepSDF method under the most important quantitative metrics.

本研究提出了一种基于局部几何代码学习的模型，通过使用图神经网络将单个可传递的潜层代码拆分成分布在 3D 形状上的一组局部潜层代码，从而改进了原始 DeepSDF 结果，并且在 3D 形状重建方面的实验中，该方法能够保留更多的细节，同时在最重要的定量指标下明显优于原始 DeepSDF 方法。

利用 SDF 学习 3D 形状局部几何编码

3D Shapes Local Geometry Codes Learning with SDF

Computer graphics, 3D computer vision and robotics communities have produced
multiple approaches to representing 3D geometry for rendering and
reconstruction. These provide trade-offs across fidelity, efficiency and
compression capabilities. In this work, we introduce DeepSDF, a learned
continuous Signed Distance Function (SDF) representation of a class of shapes
that enables high quality shape representation, interpolation and completion
from partial and noisy 3D input data. DeepSDF, like its classical counterpart,
represents a shape's surface by a continuous volumetric field: the magnitude of
a point in the field represents the distance to the surface boundary and the
sign indicates whether the region is inside (-) or outside (+) of the shape,
hence our representation implicitly encodes a shape's boundary as the
zero-level-set of the learned function while explicitly representing the
classification of space as being part of the shapes interior or not. While
classical SDF's both in analytical or discretized voxel form typically
represent the surface of a single shape, DeepSDF can represent an entire class
of shapes. Furthermore, we show state-of-the-art performance for learned 3D
shape representation and completion while reducing the model size by an order
of magnitude compared with previous work.

介绍了 DeepSDF 方法，它是用于高品质形状表示、插值和完成的一种学习连续有符号距离函数（SDF）的表示，将 3D 几何表示为体积场，并可表示整个形状类。DeepSDF 方法相比以往方法降低了一个数量级的模型大小，同时获得了学习 3D 形状表示和完成方面的最先进性能。